Critical Metals: Lessons from quantum Monte Carlo studies

Critical phenomena are one of the cornerstones of classical statistical mechanics. Quantum critical points (i.e., continuous phase transitions at zero temperature) in insulating materials is relatively well understood, being analogous to classical critical points in one spatial dimension higher. In contrast, the theory of quantum critical behavior in metals is still, to a large degree, open. Such metallic critical points are believed to play an important role in the physics of several "strongly correlated" materials, such as high temperature superconductors. Fortunately, many classes of metallic quantum critical points can be simulated efficiently using quantum Monte Carlo without the notorious "sign problem", which often hinders numerical simulations of fermionic systems. I will describe some recent progress along these lines, and how it sheds new light on some of the outstanding puzzles in the field.